Such devices are known in various embodiments, where the two conveyor tracks each have their own conveyance means (EP 581 143 B1, EP 1 161 391 B1) or a joint conveyance means (EP 581 143 B1, WO 2005/073113 A2) in the form of a continuous conveyor chain or the like. With these known storage devices, the monitoring of the elements required for function such as the conveyance means including their accessories, the transfer mechanism, etc. plus optionally the objects transported in running operation is accomplished purely visually by the operating personnel. Since the elements to be monitored are very difficult to see, in particular in the case of storage devices having a high capacity and large dimensions accordingly, it is difficult to see and track the objects, damage and malfunctions that can lead to serious consequences, damages and production downtime cannot always be detected promptly.